Align object after Motion Tracking: Edited
I do not fully understand your question, which is probably why it didn't receive much attention, but I'm still going to try to explain the problems that I do understand. 

From what I understand, you go onto explain how you tracked the object in the video, and then ask how to align it now using the tracked info. 

In the Tracking, after you have successfully tracked the object, under Reconstruction, hit Empty to Track. 

After doing this, switch back to the 3d viewport, and then you will have a bunch of empties wherever Blender thinks your trackers were. You will find that these form a box (If you have tracked successfully. Also, you may need to take footage from other angles as well, and perform the same steps on them). If you did take footage from other angles as well, then delete the overlapping empties. Now, it is just a simple matter of assigning the vertices of your box to the corresponding empties. 

Or, if that is too hard, then you could just do it by hand, which isn't too hard either. 

Again, this is pieced together by what I do understand of your problem, which isn't a lot, because your question isn't quite phrased together too well. 

I hope this solved your problem, and have a wonderful day.